In this paper the problem of sorting in various models of magnetic bubble memory systems is studied. Three basic parameters are of interest, namely, the number of steps to sort, the number of switches required, and the number of control states necessary for the switches. Several sorting algorithms are proposed with respective running times essentially n2, n/2, 1/2 n log2 n, 7/2 n, n log2n, respective numbers of switches essentially, 1, n, 2√n, 2√nlog2n , 1og2n, and respective numbers of control states essentially, 3, 2, 1/8 log2n, 1/8 log2n, and 3 log2n.